This invention generally relates to interferometry and, more particularly, to apparatus and methods for measuring the radii of curvature of optical components.
Displacement measuring interferometers (DMIs) can provide very low uncertainties in a variety of measurement applications. One disadvantage of such devices in some applications is that they have no inherent xe2x80x9czeroxe2x80x9d. In machine tool applications, for example, it is common to provide an encoder pulse or electromechanical switch to provide such a zero, albeit at greater uncertainty levels than the displacement measurement.
Phase measuring Fizeau interferometers are widely used for measuring the shape of components, such as optical surfaces, as well as transmitted wavefront and certain optical properties. Such instruments typically require a long coherence length source, which can cause problems with scattered light. In addition, the height information extracted is modulo 2xcfx80, so it is very difficult to do dimensional measurements (as opposed to surface deviation measurement) using such devices.
In advanced optics, there is a particular need to measure the radii of curvature of lenses and mirrors. Typical applications where very low uncertainties are desired in such measurements include lenses for photolithography tools that produce integrated circuits, micro-optics for telecommunications applications, etc.
Accordingly, it is a primary object of the present invention to provide an interferometric xe2x80x9czeroxe2x80x9d for DMIs.
Another object of this invention is to facilitate dimensional metrology using Fizeau interferometry.
It is a further object of this invention to provide a general self-calibration method for measuring radii of curvature.
Another object of this invention is to provide comparative, optical methods for measuring radii of curvature.
Other objects of the invention will, in part, be obvious and will, in part, appear hereinafter when the following description is read in connection with the drawings.
A self-calibration method for measuring radii of curvature of spherical optical surfaces based on measurement of three optics in pairwise combinations is provided. With a calibrated reference radius available, measurements of other radii can be made directly, given the ability to measure the internal length of an interferometric cavity.
The required measurement is made, for example, by using a delay line interferometer provided with a xe2x80x9czeroxe2x80x9d. Adding a short coherence length source and an appropriate detector to a displacement measuring interferometer makes it possible to detect (using algorithms developed for xe2x80x9cscanning white light interferometryxe2x80x9d (SWLI)) the point when the two arms of the DMI are exactly balanced. This balanced point can be used as a highly repeatable xe2x80x9czeroxe2x80x9d, or reference point for subsequent absolute length measurements.
The fixed, reference arm of the DMI is provided with some adjustment so that the reference point can be adjusted to coincide with some external (for example) mechanical reference in the specific application.
Here, a DMI is used as the delay line in a Fizeau, and the arms of the DMI are exactly balanced to obtain two coherent reflections from the reference surface and two from the test surface. The distance the DMI has to be moved to get one coherent reflection from the test surface and one from the reference surface is the internal length of the Fizeau cavity, and can be measured to very low uncertainties. SWLI can be used to identify the peak of the coherence envelope to sub-nanometer uncertainty. Hence, dimensional metrology can be performed in a Fizeau cavityxe2x80x94for examplexe2x80x94measuring thickness, flatness and parallelism in a single set up, measuring refractive index, etc.
In a spherical Fizeau cavity adjusted so that:
(1) the incident wave is exactly normal to the reference surface, so that the radius of curvature of the reference surface is exactly the radius of curvature of the wavefront; and
(2) the cavity length is adjusted so that there is no variation in average phase radially (i.e., the cavity is perfectly nulled),
the cavity length is the sum of the radii of curvature of the test and reference surfaces. When three surfaces are intercompared, pairwise, in such an architecture, the three measured lengths can be solved to give the individual radii of curvature.
The inventive algorithm may be implemented with any scheme that measures the length of the interferometric cavity. Examples include, but are not limited to, Fourier Transform Phase Shifting interferometry (FTPSI), or multi-color interferometry.